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Abstract

We measure second-harmonic generation from arrays of sub-wavelength apertures in transmission using fundamental input at 800 nm. Lattice arrangements include disordered, Penrose (quasi-periodic or aperiodic), and square (periodic). Strong angular dependence of SHG is observed, with maxima located at angular positions that roughly correspond to incidence angles of extraordinary optical transmission (EOT) for the fundamental. In addition, even at incidence normal to the sample, strong secondary maxima are observed at off-normal scattering angles for the arrangements with higher degree of order. Breaking the inversion symmetry of the aperture allows second harmonic peaks at normal incidence and detection. These measurements help to resolve the role that symmetry plays in second-harmonic generation from arrays of apertures.

Figures (13)

Fig. 1. Experimental setup for second harmonic generation measurements. The output of the Ti:Sapphire laser passes through a neutral density filter and a spectral longpass filter (690 nm) before being focused onto the sample with a 20 μm spot size by a 10 cm focal length lens; all patterned areas were larger than the spot size (the FIB sample is 25 μm by 25 μm and the e-beam samples are 80 μm by 80 μm). Emission from the sample passes through a collection lens of 10 cm focal length, a spectral short-pass filter (450 nm cutoff), a band-pass filter (400 nm center, 40 nm passband), and a 2 mm iris, and is detected with a PMT. As illustrated, θ is positive and γ is negative.

Fig. 2. SEM image of disordered array of round apertures. The apertures are roughly 235 nm by 241 nm in size. The fill fraction is about 4.6% (as calculated by image thresholding and plotting a histogram of the result). Plot of fundamental transmission (dashed linestyle) and zeroth-order SH signal (solid linestyle) as a function of incidence angle (right). Both curves are normalized to their maximum values.

Fig. 3. Second-harmonic output from disordered arrangement of circular apertures as a function of detection angle and incidence angle of the fundamental beam. Second-harmonic intensity is normalized to its’ maximum value.

Fig. 5. SEM image of square lattice of round apertures. Apertures are roughly 240 nm by 285 nm in size, with period 910 nm. The fill fraction is about 6.7%. Plot of fundamental transmission (dashed linestyle) and zeroth-order SH signal (solid linestyle) as a function of incidence angle (right). Both curves are normalized to their maximum values.

Fig. 6. Second-harmonic output from square arrangement of circular apertures as a function of detection angle and incidence angle of the fundamental beam. The SH signal is normalized to the maximum SH obtained from the disordered lattice.

Fig. 7. Image of asymmetric aperture shape (left). Angles between the three branches are intended to be 90°, 120°, and 150°, clockwise from top. The square array of asymmetric apertures has a pitch of 880 nm and fill fraction of about 3%. Plot of fundamental transmission (dashed linestyle) and zeroth-order SH signal (solid linestyle) as a function of incidence angle (right). Both curves are normalized to their maximum values.

Fig. 8. Calculated intensity distributions 5 nm below the entrance in an asymmetric aperture in 100 nm thick gold under normal illumination at 800 nm. Periodic boundary conditions are used in the calculations to mimic the square lattice. A 5 nm chromium layer is placed between the gold and substrate, overetched beneath the gold layer by 5 nm.

Fig. 9. Second-harmonic output from square arrangement of circular apertures as a function of detection angle and incidence angle of the fundamental beam. The SH signal is normalized to the maximum SH obtained from the disordered lattice.

Fig. 10. Image of Penrose arrangement of round apertures (left). Apertures are roughly 354 nm by 340 nm in size. The fill fraction is about 13%. Calculated reciprocal space (right). The diameter of each peak is indicative of its’ magnitude. The red circles represent the spatial frequencies that are used in the fitting of diffraction orders in the experimental plots, which are fx = 0,1.35,1.65,2.65,2.95, and 4.25 1/μm.

Fig. 11. Second-harmonic output from a Penrose arrangement of circular apertures as a function of detection angle and incidence angle of the fundamental beam. The SH signal is normalized to the maximum SH obtained from the disordered lattice.

Fig. 12. Plot of fundamental transmission (dashed linestyle) and zeroth-order SH signal (solid linestyle) as a function of incidence angle for the Penrose arrangement of asymmetric apertures. Both curves are normalized to their maximum values.

Fig. 13. Second-harmonic output from a Penrose arrangement of asymmetric apertures as a function of detection angle and incidence angle of the fundamental beam. The SH signal is normalized to the maximum SH obtained from the disordered lattice.